Chapter 0, Problem 51PRT

To determine

To find:the volume and the surface area of the given rectangular prism.

Answer to Problem 51PRT

  $V=60{\text{ft}}^3,S.A.=104{\text{ft}}^2$ .

Explanation of Solution

Given:

The given measurement is $\mathcal{l}=6\text{ft},\omega =2\text{ft},h=\text{5ft}$

Concept used:

volume and the surface area of the rectangular prism is given by

  $V=\mathcal{l}\omega h;S.A.=2\mathcal{l}\omega +2\omega h+2\mathcal{l}h$

Calculation:

As it is known that volume and the surface area of the rectangular prism is

  $V=\mathcal{l}\omega h;S.A.=2\mathcal{l}\omega +2\omega h+2\mathcal{l}h$ .

Therefore,

  $\begin{array}{l}V=\mathcal{l}\omega h\\ \Rightarrow V=6\text{ft}\times 2\text{ft}\times 5\text{ft}\\ \Rightarrow V=60{\text{ft}}^3\end{array}$

And

  $\begin{array}{l}S.A.=2\mathcal{l}\omega +2\omega h+2\mathcal{l}h\\ =2\times 6\text{ft}\times 2\text{ft}+2\times 2\text{ft}\times 5\text{ft}+2\times 6\text{ft}\times 5\text{ft}\\ =24{\text{ft}}^2+20{\text{ft}}^2+60{\text{ft}}^2=104{\text{ft}}^2\end{array}$

Hence, the volume and the surface area of the given rectangular prism is $V=60{\text{ft}}^3,S.A.=104{\text{ft}}^2$ .